# Calculus

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A rancher wants to fence in an area of 500000 square feet in a rectangular field and then divide it in half with a fence down the middle, parallel to one side.

What is the shortest length of fence that the rancher can use?

• Calculus -

I will set it up for you.
Let the length of the rectangle be y feet
let its width be x feet. The divider will then be x feet
So the length L
= 3x + 2y

but you know that xy = 500000
and y = 500000/x

then
L = 3x + 2(500000/x)

differentiate, set that equal to zero and solve for x
Put x back into L = ...
and you are done

• Calculus -

2345678

• Calculus -

3464.1016

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